Problem: Multiply the following complex numbers: $({-3+5i}) \cdot ({2-i})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-3+5i}) \cdot ({2-i}) = $ $ ({-3} \cdot {2}) + ({-3} \cdot {-1}i) + ({5}i \cdot {2}) + ({5}i \cdot {-1}i) $ Then simplify the terms: $ (-6) + (3i) + (10i) + (-5 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -6 + (3 + 10)i - 5i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -6 + (3 + 10)i - (-5) $ The result is simplified: $ (-6 + 5) + (13i) = -1+13i $